Some Generalized Fixed Point Theorems of Contraction Type Mappings in Quasi Metric Spaces

Abstract

This paper adjusts conditions on new defined given the name {a, d, c; r} ctype of contraction mappings on complete quasi metric space, confirms that there is only one fixed of any of these mappings with these adjustments, extends and generalizes results given in some previous research papers, and then builds a convergence theorem for a sequence of fixed points of * { } ;{ } n n N n n N S w ∈ ∈ to the unique fixed of S; w, provided that lim n→∞ S n (w) = S(w).

A Study on Common Fixed Point of Joint A;B Generalized Cyclic ϕ−abc Weak Nonexpansive Mappings and Generalized Cyclic Bakr1 2020Abstract and Applied Analysis

“…Finally, the presented results establish a simpler convergence theorem for a sequence of generalized cyclic abc ; r contraction mappings. These results are extensions and generalizations of previous results reported in[10,11,17,19,20].…”

“…Generalized Results for Generalized abc;r Contraction. Next, we generalize results for generalized abc ; r contraction[19] to those of generalized cyclic abc ; r contraction in bmetric spaces. We have the following important lemmas:Lemma 26.…”

“…Qðx, yÞ = 0 iff x = y Qðx, yÞ = Qðy, xÞ. Qðx, yÞ ≤ r ½Qðx, zÞ + Qðz, yÞ for all x, y, z ∈ XIn 2017, Bakr[19] adjusted (fp) theorem by using both b-metric spaces and generalized abc ; r contraction type of mappings.…”

Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces

“…In 2017, continuation of the generalization of cyclic weak φ of these types introduced in quasi metric spaces [3]. Definition 1.3.…”

“…If a, b, c are scalars, a, b, c ∈ [0, 1), a + b + c < 1, x = a∆, y = b∆, z = c∆ ∈ A, then scalarization metric function insures that S is reduced to the classical case of abc-generalized contraction types of mappings, see[2,3,8].More general concept is as follows. Let (C, C, q(r)) be a cone quasi metric on a Banach algebra A, ∅ = A ⊂ C and ∅ = B ⊂ C, C = A B, and S be a self mapping on C. Then S is generalized cyclic Banach algebra contraction on C with respect to the pair (A, B) iff S fulfils the following:1.…”