JUSTICE CLARK delivered the opinion of the court:

Following a jury trial in the circuit court of Cook County, defendants Roger Collins and William Bracey were convicted of armed robbery (Ill. Rev. Stat. 1979, ch. 38, par. 18-2), aggravated kidnapping (Ill. Rev. Stat. 1979, ch. 38, par. 10-2(a)(3)), and murder (Ill. Rev. Stat. 1979, ch. 38, par. 9-1(a)(1)). Pursuant to section 9-1(d) of the Criminal Code of 1961 (Ill. Rev. Stat. 1979, ch. 38, par. 9-1(d)), the State requested a death penalty hearing, which was heard by the same jury. The jury found that there were no mitigating factors sufficient to preclude a sentence of death (Ill. Rev. Stat. 1979, ch. 38, par. 9-1(g)); therefore, the court sentenced the defendants to death.

On direct appeal to this court (73 Ill.2d R. 603), the convictions and sentences were affirmed. ( People v. Collins (1985), 106 Ill.2d 237 ( Collins I).) A petition for rehearing in this court was denied, and the United States Supreme Court denied the defendants' petition for writ of certiorari.

On May 2, 1986, the defendants filed a joint petition under the Post-Conviction Hearing Act (Ill. Rev. Stat. 1985, ch. 38, par. 122-1 et seq.). The State filed a motion to dismiss the petition, to which the defendants filed a response. On March 21, 1991, the trial judge dismissed the petition without an evidentiary hearing. Review of the post-conviction petition for relief raises one issue: Did the trial court err in denying the post-conviction petition?

The facts relating to the underlying crimes will not be set out in their entirety, as a comprehensive review of the evidence is contained in Collins I and the defendants do not maintain that their convictions were not supported by the evidence. Rather, relevant facts will be discussed as they are germane to the issues on review.

The defendants first argue that they were deprived of a fair trial and an impartial jury by the presence on the jury of the wife of an appellate court judge who had sentenced one of the defendants in an earlier conviction when the judge was sitting on the circuit court.

During voir dire, one of the venirepersons, Dorothy Downing, stated that she was the wife of an Illinois appellate judge sitting in the first district. She also stated that her husband had formerly been a judge on the circuit court of Cook County. When questioned by the trial judge in this matter, Downing stated that the fact that her husband was an appellate judge would have no effect upon her consideration of the defendants' case and that she could be fair and impartial. She was accepted by both counsel as a juror.

No objection was raised to Downing's presence on the jury during trial. However, on direct appeal to this court, the defendants argued that her presence on the jury was per se prejudicial, requiring that their convictions be set aside. This court concluded that the defendants had waived the issue for purposes of review.

When a defendant has previously taken a direct appeal, all matters which were raised or which could have been raised on that direct appeal are res judicata in his subsequent post-conviction proceeding. ( People v. Neal (1990), 142 Ill.2d 140, 146.) "Determinations of the reviewing court on the prior direct appeal are res judicata as to issues actually decided and issues that could have been presented on direct appeal and that were not are deemed waived." ( People v. Albanese (1988), 125 Ill.2d 100, 105.) Although a dissent filed in Collins I made essentially the same argument that the defendants are now presenting to this court (see Collins, 106 Ill.2d at 289 (Clark, C.J., dissenting, joined by Simon, J.)), we recognize that the majority found the question of Downing's presence on the jury to have been waived by the defendants. Therefore, the issue is res judicata.

Defendants next allege that the prosecution improperly used peremptory challenges to systematically exclude prospective black jurors from sitting on the jury. In Batson v. Kentucky (1986), 476 U.S. 79, 97-98, 90 L.Ed. 2d 69, 88-89, 106 S.Ct. 1712, 1723-24, the United States Supreme Court held that a prosecutor's use of the peremptory challenge to exclude blacks from a jury trying a black defendant may be the basis for an equal protection challenge. Following its opinion in Batson, the Court held that its rule applies to cases pending on direct review at the time Batson was decided. ( Griffith v. Kentucky (1987), 479 U.S. 314, 93 L.Ed.2d 649, 107 S.Ct. 708.) The Batson opinion did not, however, apply to cases on collateral review. ( Allen v. Hardy (1986), 478 U.S. 255, 92 L.Ed.2d 199, 106 S.Ct. 2878.) Since this case was not pending on direct appeal at the time Batson was decided, Batson is inapplicable. People v. Davis (1987), 119 Ill.2d 61, 64.

The standard under which the defendants' claim is to be reviewed is that found in the Supreme Court's opinion in Swain v. Alabama (1965), 380 U.S. 202, 227, 13 L.Ed.2d 759, 776, 85 S.Ct. 824, 839 ("[T]he defendant must, to pose the issue, show the prosecutor's systematic use of peremptory challenges against Negroes over a period of time"). Although the holding in Swain was based on fourteenth amendment guarantees, this court has held that "the authority of Swain was not lessened because of the recognition of a sixth amendment fair-cross-section requirement in Taylor v. Louisiana (1975), 419 U.S. 522, 42 L.Ed.2d 690, 95 S.Ct. 692." People v. Williams (1983), 97 Ill.2d 252, 278.

In their post-conviction petition, the defendants did not raise any claim of the case-by-case exclusion of blacks required by Swain nor have they submitted any affidavits or made any sort of showing of this practice. The mere allegation of an equal protection challenge without more is insufficient to warrant an evidentiary hearing on the issue. Accordingly, we conclude that the defendants have failed to provide any basis upon which post-conviction relief can be granted on this issue.

The defendants next argue that they were denied effective assistance of counsel. Strickland v. Washington (1984), 466 U.S. 668, 80 L.Ed.2d 674, 104 S.Ct. 2052, established the standard by which claims of ineffective assistance of counsel are to be measured. A defendant must show (1) counsel's performance was so seriously deficient as to fall below an objective standard of reasonableness under prevailing professional norms and (2) that the deficient performance so prejudiced the defense as to deny the defendant a fair trial. Strickland, 466 U.S. at 687, 80 L.Ed.2d at 693, 104 S.Ct. at 2064.

In the present matter, the defendants first argue that counsel's failure to object at trial to the presence of Downing on the jury amounted to ineffective assistance of counsel. The defendants also argue that it was incompetent of counsel to reveal to the jury that Judge Downing sentenced Bracey to the penitentiary in 1970. Knowing that Bracey had an extensive criminal history, trial counsel had him testify as to the extent of his convictions on direct examination rather than have the information brought to the attention of the jury on cross-examination. In so doing, it was revealed to the jury that Judge Downing had sentenced Bracey to serving time in the penitentiary in 1970.

Both of these examples the defendants rely on as instances of counsel's ineffectiveness were considered and rejected by this court in Collins I. ( Collins, 106 Ill.2d at 273.) With respect to the first argument, this court stated that both attorneys were in a better position than this court, based simply on a review of "a cold record," to assess Downing's demeanor in response to questions from the court about her ability to be a fair and impartial juror. As both attorneys accepted Downing as a juror, knowing her relationship to Judge Downing, this court was unable to determine that their decision was unreasonable. Likewise, this court considered the defendants' second claim under the Strickland standard of ineffective assistance of counsel and concluded that, while defense counsel's mention of Judge Downing in connection with one of Bracey's prior convictions was "an error in judgment," it was not so substantial an error that defense counsel failed to "`function as the "counsel" guaranteed the defendant by the Sixth Amendment.'" ( Collins, 106 Ill.2d at 273, quoting Strickland, 466 U.S. at 687, 80 L.Ed.2d at 693, 104 S.Ct. at 2064.) Although we note that the dissent in Collins I concluded otherwise on both of these issues (see Collins, 106 Ill.2d at 288 (Clark, C.J., dissenting, joined by Simon, J.)), we abide by our original decision on the matter. Accordingly, we find that both these issues are res judicata for purposes of this petition.

The defendants next argue that counsel was ineffective for failing to preserve facts concerning the racial makeup of the jury. The defendants have offered no affidavits or made any sort of showing in support of their allegations, simply requesting that an evidentiary hearing be granted at which they could demonstrate the alleged error. Under the Post-Conviction Hearing Act, a defendant is not entitled to a hearing as a matter of right, but only where the allegation of a substantial violation of constitutional rights is supported by the record or by affidavits accompanying the petition. ( Albanese, 125 Ill.2d at 105.) We conclude that the defendants have failed to establish a substantial deprivation of constitutional rights. People v. Del Vecchio (1989), 129 Ill.2d 265, 284; People v. Griffin (1985), 109 Ill.2d 293, 303.

The defendants next argue under this heading three other matters which they claim show inadequacy of counsel under the Strickland standards. These matters are not set out with any particularity and are unaccompanied by any supporting material. For instance, the defendants argue that "various actions and inactions relied upon by [this court] to find `waiver' on direct appeal" are as a result of the trial counsel's ineffective assistance. The defendants do not refer to the specific "actions or inactions" this court concluded in Collins I that the defendants had waived. The allegation is so unspecific as to merit no consideration by this court.

The defendants also argue that defense counsel's "failure to bring out mitigating evidence at sentencing" was ineffective. This argument is, we assume, based on the assumptions that (1) mitigating evidence existed and (2) that the evidence would have led to a different result at the sentencing phase of the defendant's trial. The defendants have failed to demonstrate that such mitigating evidence exists (see, e.g., People v. Holman (1989), 132 Ill.2d 128, 167), and because the defendants have not proven otherwise, we shall assume that trial counsel's failure to produce such evidence was because it did not exist.

The defendants' next argument under this heading is that the trial counsel was ineffective for failing to impeach a prosecution witness with his grand jury testimony. This argument is res judicata, as it was considered and rejected by this court on direct appeal. Collins, 106 Ill.2d at 273.

The defendants' last argument under this heading is that their counsel on direct appeal (the same as at trial) was ineffective for not alleging with more specificity the errors not brought to the attention of the trial court and to this court on direct appeal. The defendants again fail to point with any specificity to specific instances of ineffective counsel which this court could examine under the Strickland standards. The defendants simply allege that the trial counsel was "ineffective for failing to assert trial counsel's ineffectiveness more specifically than was done on direct appeal."

The defendants are incorrect in their allegations on many grounds. First, as was discussed above, many of the instances of ineffective assistance of counsel the defendants point to in their post-conviction petition were in fact made on direct appeal and are res judicata. Second, this court has long recognized that counsel on appeal has no obligation to raise every conceivable argument which might be made, and counsel's assessment of what to raise and argue will not be questioned unless it can be said that his judgment in this regard was patently erroneous. People v. Frank (1971), 48 Ill.2d 500, 505.

Finally, the defendants have failed to refer to specific actions or arguments the trial counsel should have made. Under the standards laid out in Strickland, the defendant must point to a specific act or omission of counsel which he alleges shows prejudice or unprofessional error. ( Strickland, 466 U.S. at 690, 80 L.Ed.2d at 695, 104 S.Ct. at 2066.) The vague allegation that counsel could have done more on appeal is insufficient under Strickland to properly allege ineffective counsel. Accordingly, we conclude that the defendants did not raise a substantial deprivation of constitutional rights.

The defendants next raise several challenges to the constitutionality of the Illinois death penalty statute (Ill. Rev. Stat. 1985, ch. 38, par. 9-1). The defendants argue that the statute is unconstitutional because it gives prosecutors standardless discretion to seek the death penalty, resulting in arbitrary imposition of capital punishment; the jury is permitted to consider nonstatutory aggravating factors; there is no provision for meaningful appellate review; and it puts on the defendant the burden of showing why the death penalty should not be imposed. The first three arguments the defendants raise were considered and rejected by this court in Collins I and are, therefore, res judicata. Collins, 106 Ill.2d at 285.

As to the defendants' final argument, we conclude that this too was considered and rejected by this court in Collins I. There, the defendants advanced what we believe is the converse of the argument they are now presenting to this court. In Collins I, the defendants argued that the Illinois death penalty statute was unconstitutional because it fails to require the prosecution to prove beyond a reasonable doubt that there were no mitigating factors sufficient to preclude imposition of the death penalty. ( Collins, 106 Ill.2d at 285.) This court rejected the defendants' argument. Collins, 106 Ill.2d at 285; see also People v. Garcia (1983), 97 Ill.2d 58, 80-81.

Here, the defendants argue that the death penalty statute is unconstitutional because it places on the defendant the burden of showing why the death penalty should not be imposed. As we stated above, we believe this argument is simply the converse of the argument the defendants advanced in Collins I. Therefore, we conclude that this issue is res judicata for purposes of our review.

The defendants next allege that they were deprived of a fair trial and of a fair and impartial jury because the qualification of prospective jurors pursuant to Witherspoon v. Illinois (1968), 391 U.S. 510, 20 L.Ed.2d 776, 88 S.Ct. 1770, resulted in a conviction-prone jury. Again, this argument is res judicata for purposes of our review. ( Collins, 106 Ill.2d at 278.) Moreover, although the defendants argue that the trial court improperly denied their petition without a hearing in light of their averments that "newly-available statistical evidence demonstrating that `death-qualified' jurors are conviction prone," the defendants failed to tender this evidence with their petition. This unsupported allegation supplied no ground for the granting of a hearing.

The defendants next argue that the prosecution knowingly used perjured testimony in violation of due process of law. The defendants maintain that "the prosecution was well aware of Nellum's [the witness'] prior inconsistent statement, yet put him on to testify without turning such statement over to the defense." The defendants argue that the prior inconsistent statement was not "discovered until long after the defendants' trial."

The defendants do not identify the "prior inconsistent statement" that was allegedly introduced in violation of the defendants' due process rights. Nellum was the chief prosecution witness, who admittedly participated in the crimes. During his direct examination, Nellum stated that he had been with Collins when Collins threw the guns used in the murders into Lake Michigan. On cross-examination, Nellum admitted that he had told the police during his initial interrogation that he did not know where the guns could be found. ( Collins, 106 Ill.2d at 252-53.) During his grand jury testimony, Nellum was not asked about his knowledge concerning the location of the guns, nor did he volunteer any information on the matter. Collins, 106 Ill.2d at 272.

If we are to assume that the "inconsistent statement" to which the defendants refer is Nellum's statement to the police that he did not know of the whereabouts of the gun when in fact he did, we conclude that the defendants have failed to provide any evidence in support of their allegation that the prosecution knowingly used perjured testimony. Neither have the defendants presented any support for their position that the prosecution intentionally withheld information regarding Nellum's statements to the police from the defense. Even if we were to accept the defendants' position, they were aware of Nellum's inconsistent statements at the time of their direct appeal and they failed to raise a due process challenge at that time. Accordingly, the issue is res judicata for purposes of this review.

The defendants next argue that certain arguments made by the prosecution at their trial were improper and prejudicial. The defendants argue that a statement made by the prosecution in closing insinuated that Nellum had made a prior consistent statement; that the prosecutor improperly suggested that defense counsel had impugned his integrity; and that a statement made by the prosecutor at the second stage of the death penalty hearing analogized the jury's duty to impose the death penalty to killing during a war. All of these remarks were raised and considered on the defendants' direct appeal and are res judicata.

Additionally, the defendants argue that the prosecution made "unfair attack[s] on defense counsel," without specifying the nature of the comments. The defendants simply refer to the transcript of the trial. Again, the defendants are not entitled to a hearing by merely alleging that a violation of their constitutional rights occurred at trial or on direct appeal. The allegations must be supported by the record or by affidavits accompanying their petition. The defendants have failed to meet this burden; therefore, we conclude that they have not alleged a proper basis on which post-conviction relief can be granted on this issue.

Finally, the defendants challenge the trial court's ruling on two motions filed, one motion requesting funds to hire an investigator and the other requesting leave to file a subpoena. In their motion for funds to hire an investigator, the defendants argued that the funds were necessary to hire an investigator to, inter alia, take statements from jurors on the defendants' case to ascertain the impact, if any, that resulted from the presence of the judge's wife on the jury, as well as to determine the racial composition of the jury venire. The latter request was to determine whether the prosecution had exercised its peremptory challenges in violation of Batson. The circuit court denied the motion.

The defendants then filed a motion for an order granting leave to subpoena the jury supervisor to compel the production of the jury records of all the jurors who were called and questioned. This motion was also denied. The defendants now argue that the trial judge improperly denied their motions.

The granting of the defendants' motions was within the discretion of the trial judge. ( People v. Lear (1991), 143 Ill.2d 138, 147-49; see also People ex rel. Daley v. Fitzgerald (1988), 123 Ill.2d 175, 180-83.) His order will not be overturned unless there is a showing that the decision was manifestly erroneous. ( People v. Del Vecchio (1989), 129 Ill.2d 265, 284; see also People ex rel. Daley v. Fitzgerald (1988), 123 Ill.2d 175, 180-83.) The defendants have offered no materials in support of this conclusion.

Moreover, we note that after the trial judge denied the defendants' motions, the defendants sought a supervisory order from this court directing the trial judge to allow for the expenditure of up to $1,000 for the hiring of a private investigator. This court issued an order on May 8, 1989, denying the defendants' motion. We believe that our order denying the defendants' supervisory order as well as our decision on this issue are correct.

The circuit court did not err in denying the defendants' petition for post-conviction relief, and its judgment is affirmed.

The clerk of this court is directed to enter an order setting Tuesday, March 23, 1993, as the date on which defendant Collins' death sentence, entered in the circuit court of Cook County, is to be carried out. Defendant shall be executed in the manner provided by law (Ill. Rev. Stat. 1985, ch. 38, par. 119-5). The clerk of this court shall send a certified copy of the mandate in this case to the Director of Corrections, the warden at Stateville Correctional Center, and the warden of the institution in which defendant Collins is confined.

The clerk of this court is directed to enter an order setting Tuesday, March 23, 1993, as the date on which defendant Bracey's death sentence, entered in the circuit court of Cook County, is to be carried out. Defendant shall be executed in the manner provided by law (Ill. Rev. Stat. 1985, ch. 38, par. 119-5). The clerk of this court shall send a certified copy of the mandate in this case to the Director of Corrections, the warden at Stateville Correctional Center, and the warden of the institution in which defendant Bracey is confined.

Affirmed.