Fixed points for non‐surjective expansion mappings

Abstract

The contractive conditions of Popa (Demonstr. Math. 1990, 23, 213-218) were further improved for four non-surjective expansion mappings, and some common fixed point theorems under semi-compatible pairs of mappings are proved. Our main findings bring improvements to a number of results in the non-metric setting. Some implications for mathematical physics are raised with respect to physical invariants.

Semicompatibility and fixed point theorems in fuzzymetric space using implicit relation

“…Saliga [9] and Sharma et. al [10] proved some interesting fixed point results using implicit real functions and semicompatibility in d-complete topological spaces. Recently, Popa in [8] used the family F 4 of implicit real functions to find the fixed points of two pairs of semicompatible maps in a d-complete topological space.…”

Semicompatibility and Fixed Point Theorem in Fuzzy Metric Space Using Implicit Function

“…Saliga [9] and Sharma et. al [10] proved some interesting fixed point results using implicit real functions and semicompatibility in d-complete topological spaces. Recently, Popa in [8] used the family of implicit real functions to find the fixed points of two pairs of semicompatible maps in a d-complete topological space.…”

“…By putting 2,nxxyw== in (4) We obtain ()()()(){}2222,,min,,,,,,,,nnnnMAxBwktMSxTwtMAxSxtMBwT wkt≥ Taking limit as and using (5) we get n→∞ ()(){},,min1,1,,,MuBwktMBwukt≥ We have for all (),,MuBukt≥ 0t> Hence (),,MuBut= Thus u Bw= Therefore BwTwu== Since is weak compatible. (,BT We get TBwBTw= that is (10) .BuTu=…”