Discussions on Recent Results forα-ψ-Contractive Mappings

Abstract

We establish certain fixed point results forα-η-generalized convex contractions,α-η-weakly Zamfirescu mappings, andα-η-Ćirić strong almost contractions. As an application, we derive some Suzuki type fixed point theorems and certain new fixed point theorems in metric spaces endowed with a graph and a partial order. Moreover, we discuss some illustrative examples to highlight the realized improvements.

A new approach to the study of fixed point theory for simulation functions in G-Metric spaces

“…The well-known Banach Contraction Principle [1] ensures the existence and uniqueness of a fixed point of a contraction on a complete metric space. After this principle, several authors generalized this principle by introducing the various contractions on metric spaces [2,[3][4][5][6][7][8][9]. In this work, we introduce a mapping namely simulation funtion and the notion of Z-contraction.…”

Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations

“…where α: X × X → [0, ∞) and proved some fixed point results for such mappings in the context of complete metric spaces (X, d). Subsequently, Salimi et al [6] and Hussain et al [2,7] modified the notions of α-ψ-contractive, α-admissible mappings and proved certain fixed point results. In 2014, Jleli et al [4] generalized the contractive condition by considering a function Θ: (0, ∞) → (1, ∞) satisfying, (Θ 1 ) Θ is nondecreasing; (Θ 2 ) for each sequence {α n } ⊆ R + , lim n→∞ Θ(α n ) = 1 if and only if lim n→∞ (α n ) = 0;…”

Fixed Point Theorems for Manageable Contractions with Application to Integral Equations

“…The Banach contraction principle [1] is an elementary result in metric fixed point theory. This golden principle has been broadened in several directions by different authors (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). An interesting generalization is the elongation of the Banach contraction principle to multivalued maps, known as Nadler's fixed point theorem [19] and Mizoguchi-Takahashi's fixed point theorem [20].…”