Triple fixed point theorems via α-series in partially ordered metric spaces

Abstract

This manuscript has two aims: first we extend the definitions of compatibility and weakly reciprocally continuity, for a trivariate mapping F and a self-mapping g akin to a compatible mapping as introduced by Choudhary and Kundu (Nonlinear Anal. 73:2524-2531) for a bivariate mapping F and a self-mapping g. Further, using these definitions we establish tripled coincidence and fixed point results by applying the new concept of an α-series for sequence of mappings, introduced by Sihag et al. (Quaest. Math. 37:1-6, 2014), in the setting of partially ordered metric spaces. MSC: 54H25; 47H10; 54E50

Tripled Fixed Point Approaches and Hyers-Ulam Stability With Applications

“…In 1987, Guo and Lakshmikantham [7] presented the concept of a coupled FP for continuous and discontinuous operators in reference to triple quasi solutions of an initial value problem for ordinary differential equations. Several authors concentrated on these ideas and utilized the findings to discuss if certain problems have solutions; for more information, see [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Solving a System of Differential Equations with Infinite Delay by Using Tripled Fixed Point Techniques on Graphs

“…The (TFP) theory has a large number of significant applications that have been successfully employed to address a wide variety of issues. Researchers have focused on these issues to examine possible solutions, as seen in [2][3][4][5][6][7].…”

A Tripled Fixed Point Theorem in C ∗ -Algebra-Valued Metric Spaces and Application in Integral Equations

“…Let A ∈ M q,q ðAÞ, then A is said to be convergent to zero, iff A n goes to θ as n ⟶ ∞. See [5][6][7][8] for more details.…”