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We initiate a new function, referred to as a controlled metric space of type (γ β), through the use of the functions γ β: MM! M to play a key role in the triangular inequality. Our new concept is to extend the idea of the extended bmetric space in the sense of Kamran et al. to a more general type. We base and prove new results on fixed points in such spaces. Also, we give some examples to reinforce our concept and related results.. [ABSTRACT FROM AUTHOR]

In this paper, we take advantage of implicit relationships to come up with a new concept called "Aϑ-α-contraction mapping". We utilized our new notion to formulate and prove some common fixed point theorems for two and four self-mappings over complete extended quasi b-metric spaces under a set of conditions. Our main results widen and improve many existing results in the literature. To support our research, we present some examples as applications to our main findings. [ABSTRACT FROM AUTHOR]

Ali, Dinu, and Petrescu (M. U. Ali, S. Dinu, and L. Petrescu, Existence of fixed points of set-valued maps on modular b-gauge spaces, U.P.B. Sci. Bull., Series A, Vol. 82, Iss. 4, 2020, ISSN 1223-7027) introduced the notion of modular b-gauge spaces induced through the family of pseudomodular b-metrics and showed the existence of fixed point on this space. In this paper, we employ the notion of modular b−gauge spaces to prove the existence of common fixed points of set-valued maps. Precisely, we formulate and prove two different theorems. Also, we state some corollaries. Moreover, we give an example to illustrate the validity of our results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some fixed point results for a mapping satisfying generalized (ɸ, ψ)-contractive condition in a complete partially ordered b-metric space. Also, we prove some coincidence fixed point results for two self mappings S and f on a set X under a set of conditions, where S satisfies a generalized (ɸ, ψ)-contractive condition with respect to a function f in a complete partially ordered b-metric space. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. A few examples are illustrated to support our results. [ABSTRACT FROM AUTHOR]

Tallafha, A. and Alhihi S. in [15], asked the following question. If f is a contraction from a complete semi-linear uniform space (X, G) to it self, is f has a unique fixed point. In this paper, we shall answer this question negatively and we shall show that convex metric space and Mspace are equivalent except uniqueness. Also, we shall characterize convex metric spaces and use this characterization to give some application using semi-linear uniform spaces. [ABSTRACT FROM AUTHOR]

Semi-linear uniform space is a new space defined by Tallafha. A and Khalil, R in [7]. The authors studied some cases of best approximation in such spaces, and gave some open problems in uniform spaces. Besides they defined a set valued map ρ on X x X and asked two questions about the properties of ρ. In 2011, Tallafha [8] defined another set valued map δ on X x X, and give more properties of semi-linear uniform spaces using the maps ρ, δ and he answered the questions about ρ. The purpose of this paper is to introduce some open questions concerning this new spaces. [ABSTRACT FROM AUTHOR]