These consolidated proceedings relating to domestic-relations matters stem from a judgment of the Elmore Circuit Court divorcing Twanda R. Williams (“the mother”) and Terry Williams (“the father”), who are the parents of twin daughters *355born in June 1988. That judgment was entered in case no. DR-06-282 (“the divorce action”) in February 2008, after the daughters had reached the age of majority in Alabama (see Ala.Code 1975, § 26-1-1(a)); the judgment, in pertinent part, did not contain any provision regarding the custody of the daughters or regarding parental support thereof, but it did mandate various financial awards to the mother in the nature of alimony and divisions of marital property. The mother, acting through counsel, filed a motion to alter, amend, or vacate the judgment, asserting that an award of postminority support pursuant to the holding of Ex parte Brewington, 445 So.2d 294 (Ala.1983), was due to be made to the mother as the daughters’ caregiver because of their having been diagnosed as having social, emotional, and language-functioning disabilities, as well as depression and Asperger’s Syndrome (ie., an autism-spectrum disorder). The trial court, after a hearing on the mother’s post-judgment motion, partially granted the mother’s motion and reopened its judgment as to certain property-division matters; however, although the trial court indicated that it would take the issue of postminority support “under advisement,” its subsequent order of September 4, 2008, amending the divorce judgment did not include an award of postminority support because the daughters were “not in school” (although the father was directed therein to include the daughters in his “Survivor Benefit Plan,” ie., to name them as pension beneficiaries). Notably, the mother did not appeal from the judgment entered in the divorce action, as finally amended.
The parties soon found themselves before the trial court again regarding enforcement matters; although the record contains certain filings from an action numbered as case no. DR-06-232.01, the principal litigation activity that is pertinent to the mother’s appeal (this court’s case no. 2120796) occurred in the trial court’s case no. DR-06-232.02, an action initially brought by the father seeking modification of his alimony and retirement-benefit-payment obligations. The mother asserted a counterclaim alleging that the father was in contempt of his obligations under the divorce judgment as amended and sought a declaration mandating that the father take measures to ensure coverage of the daughters under the military health-insurance plan known as TRICARE. After those pleadings were filed, counsel for both parties were permitted to withdraw, and the parties thereafter represented themselves in case no. DR-06-232.02 without the benefit of legal counsel. The trial court initially entered an order assessing the father’s monetary arrearage; subsequently, the father was determined to be in contempt and directed to pay a sum certain to purge himself. The trial court later addressed the remaining issues raised by the pleadings in case no. DR-06-232.02 in a judgment dated February 14, 2013; the trial court declared that the mother was entitled to receive one-half the father’s gross retirement-benefit payments before reductions (implicitly denying the father’s relief requests) and that the father would be required to place the daughters on his TRICARE coverage “for as long as it remain[ed] available to them.”
Although the order and judgment discussed above addressed the issues framed by the pleadings in case no. DR-06-232.02, the mother’s appeal in case no. 2120796 asserts error as to the trial court’s alleged failure in that action to award Brewington support.1 The mother’s injec*356tion of the issue into ease no. DR-06-282.02 occurred, if at all, by means of a document labeled “Case Review” addressed to the trial court and dated February 8, 2013, in which she requested an award of postminority support; there is no indication in that document that it had been served upon the father, nor did the mother seek leave of the trial court in that document to amend her mother’s nearly four-year-old counterclaim.
Regardless of our view of the merits of the mother’s appeal in case no. 2120796, we lack jurisdiction to consider her appeal, and therefore must dismiss it, because the mother filed her notice of appeal from the trial court’s February 14, 2013, judgment on June 13, 2013, more than 42 days after that judgment was entered. See Rules 2(a)(1) and 4(a)(1), Ala. R.App. P. Although the mother claims to have timely filed a motion pursuant to Rule 59(e), Ala. R. Civ. P., that would have suspended the time for taking an appeal pursuant to the provisions of Rule 4(a)(3), Ala. R.App. P., the supplemental record she has caused to be transmitted to this court reveals that the document she claims to have filed with the trial court within 30 days after the entry of the trial court’s February 14, 2013, judgment (which document is, like the February 8, 2013, document, labeled simply “Case Review”) was sent to that court on February 27, 2013, via facsimile transmission. Under the holding of our supreme court in Ex parte Tuck, 622 So.2d 929 (Ala.1993), a party cannot effectively “ ‘file’ a notice of appeal or other paper with an Alabama court clerk by transmitting it to the clerk’s office by facsimile transmission.” L.M. v. Shelby Cnty. Dep’t of Human Res., 999 So.2d 505, 507 (Ala.Civ.App.2008). Further, the electronic case-action-summary sheet maintained by the clerk of the trial court in case no. DR-06-232.02 does not reflect that the document relied upon by the mother as having constituted a post-judgment motion was ever filed with that court.
Following the entry of the trial court’s February 14, 2013, judgment, the father retained counsel and initiated in the trial court a new civil action, identified as case no. DR-06-232.03, in which he sought the termination of garnishment orders regarding alimony and the deletion of the requirement that he place the daughters on his TRICARE coverage because he was not providing 50% of the daughters’ support and armed-services guidelines would, therefore, not allow the daughters to be enrolled in TRICARE. The mother filed a response in which she asserted that the trial court should not address Brewington support and should not disturb the TRI-CARE health-insurance requirement because of the pending appeal in case no. 2120796 but stated that the father had not included the daughters in his Survivor Benefit Plan in conformity with the September 4, 2008, amended divorce judgment and that he should be directed to do so. After a hearing, the trial court entered an order on January 8, 2014, declaring that the father was not required to provide TRICARE coverage for the daughters and that “[t]here is no medical insurance premium requirement on the father”; on January 9, 2014, the trial court entered a *357second order lifting the garnishment of the father’s funds and stating that the father’s payments due under the property division set forth in the divorce judgment as amended would be paid at a rate of $922 per month from the father’s retirement benefits. Neither order addressed Brew-ington support or the daughters’ inclusion in the father’s Survivor Benefit Plan.
The mother filed a petition for a writ of mandamus within a presumptively reasonable time after the entry of the two January 2014 orders of the trial court. The three-page body of her petition seeks an order directing the trial court to (a) immediately rule that the daughters are entitled to Brewington support; (b) vacate the January 8, 2014, order setting aside the father’s duty to ensure that the daughters are covered under TRICARE; (c) enforce that portion of its September 4, 2008, judgment mandating that the daughters be included in the father’s Survivor Benefit Plan so as to “allow [them] to receive an annuity in[ ] case of [the] father’s death”; and (d) award the mother $500,000 to be deposited in two particular irrevocable supplemental-care trust accounts. The mother’s petition was assigned case no. 2130383 by this court. We called for an answer from the respondents, and after having received an answer from the father, case no. 2130383 was consolidated with case no. 2120796 and was submitted for a decision.
Our review of the mother’s mandamus petition leads us to the conclusion that it is without merit. The mother’s petition cites only two cases, both in support of her first issue regarding Brewing-ton support — Brewington itself and Ex parte Cohen, 763 So.2d 253 (Ala.1999), which held that Brewington support, when awarded, is to be calculated pursuant to the provisions of Rule 32, Ala. R. Jud. Admin. The mother’s petition does not cite authority for the other three issues raised therein, in contravention of Rule 21(a)(1)(D), Ala. R.App. P., which, similar to the analogous Rule 28(a)(10), Ala. R.App. P., governing briefs in appeals, requires a petition for an extraordinary writ filed in an appellate court to cite statutes and authorities supporting the proposition that the writ should issue; as our supreme court stated in Ex parte Showers, 812 So.2d 277, 281 (Ala.2001), “[i]f anything, the extraordinary nature of a writ of mandamus makes the Rule 21 requirement of citation to authority even more compelling than the Rule 28 requirement of citation to authority in a brief on appeal.” Moreover, as to the sole issue properly presented by the mother, we conclude that the mother’s insistence in case no. DR-06-232.03 that the trial court should not address Brew-ington support precludes her from seeking a writ compelling an award of such support, based upon invited error and the mother’s failure to have requested the trial court to perform the act sought in her mandamus petition. See Ex parte City of Prattville, 56 So.3d 684, 689-90 (Ala.Civ.App.2010).
In light of the foregoing facts and authorities, we dismiss the mother’s appeal in case no. 2120796 and deny the mother’s petition for mandamus relief in case no. 2130383.
2120796 — APPEAL DISMISSED.
2130383 — PETITION DENIED.
THOMPSON, P.J., and PITTMAN, THOMAS, and DONALDSON, JJ., concur. MOORE, J., concurs in the result, without writing.. Although certain sections of the mother's appellate brief in case no. 2120796 purport to assert error with respect to the trial court's failure to award her a health-insurance ar-*356rearage based upon the trial court’s September 4, 2008, judgment directing the father to include the daughters in his Survivor Benefit Plan, the mother's argument does not cite any legal authority pertinent to that issue. When an appealing party fails to cite any authority for an argument on a particular issue, an appellate court may deem that issue waived because it is neither the appellate court's duty nor its function to perform that party's legal research, even when the party is acting pro se. See Schwartz v. Schwartz, 835 So.2d 1017, 1018 (Ala.Civ.App.2002) (citing Rule 28, Ala. R.App. P.).