Fixed points of Suzuki-type generalized multivalued (f,θ,L)- almost contractions with applications

Abstract

In this paper, we define Suzuki type generalized multivalued almost contraction mappings and prove some related fixed point results. As an application, some coincidence and common fixed point results are obtained. The results proved herein extend the recent results on fixed points of Kikkawa Suzuki type and almost contraction mappings in the frame work of complete metric spaces. We provide examples to show that obtained results are proper generalization of comparable results in the existing literature. Some applications in homotopy, dynamic programming, integral equations and data dependence problems are also presented. H(A, B) = inf ε D(A, B) if D(A, B) φ, ∞ if D(A, B) = φ.

On Complex-Valued Triple Controlled Metric Spaces and Applications

“…Since the breakthrough of Banach [1] in 1922, where he was able to show that a contractive mapping on a complete metric space has a unique fixed point, the field of fixed point theory has become an important research focus in the field of mathematics; see [2][3][4][5][6]. Due to the fact that fixed point theory has many applications in many fields of science, many researchers have been working on generalizing his result by either generalizing the type of contractions [7][8][9][10] or by extending the metric space itself (b-metric spaces [11,12], controlled metric spaces [13], double controlled metric spaces [14], etc.). On the other hand, Azam et al [15] defined complex-valued metric spaces and gave common fixed point results.…”

Common Fixed-Point Theorems of Generalizedψ,φ−Weakly Contractive Mappings inb−Metric-Like Spaces and Application

“…is celebrated principle has been generalized by several authors. Recently, Saleem et al [2] obtained fixed-point results of Suzuki-type generalized multivalued (f, θ, L)-almost contractions and coincidence and common fixed-point results of Suzuki-type generalized multivalued (f, θ, L)-almost contraction mapping in the setting of metric spaces. In 2019, Li et al [3] defined a new contractive-type mapping called Z θ -contraction and proved some fixed-point and Suzukitype fixed-point results in the context of complete metric spaces.…”

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“…The importance of fixed point theory emerges from the fact that it gives a unified approach and constitutes an essential tool in resolving problems which are not necessarily linear. A variant number of problems can be expressed as nonlinear equations of the form f ðuÞ = u, where f is a self-mapping, see [1][2][3][4][5][6]. Nevertheless, an equation of the type f ðuÞ = u does not necessarily have a solution if f is a non-self-mapping.…”