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In the present study, we prove generalizations of Banach, Kannan, Chatterjea, Čirič-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mapping contracting perimeters of triangles. We consider corresponding mappings in semimetric spaces with triangle functions introduced by Bessenyei and Pâles. Such an approach allows us to derive corollaries for various types of semimetric spaces such as metric spaces, ultrametric spaces, and b-metric spaces. The significance of these generalized theorems extends across multiple disciplines, such as optimization, mathematical modeling, and computer science. They may serve to establish stability conditions, demonstrate the existence of optimal solutions, and improve algorithm design. [ABSTRACT FROM AUTHOR]

Let X be a class of metric spaces and let Px be the set of all f: [0, oo) [0, oo) preserving X, i.e., (/, f o p) e X whenever (/, p) e X. For arbitrary subset A of the set of all metric preserving functions, we show that the equality Px = A has a solution if A is a monoid with respect to the operation of function composition. In particular, for the set SI of all amenable subadditive increasing functions, there is a class X of metric spaces such that Px = SI holds. 2020 Mathematics Subject Classification: Primary 26A30, Secondary 54E35, 20M20 [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalizations of the concept of MR-Kannan type contractions and utilize those conditions to derive new fixed point theorems under both contractive and non-contractive conditions. Our approach enhances various existing results related to enriched mappings. [ABSTRACT FROM AUTHOR]

In this note we point out errors in the proofs of first two theorems contained in Demonstratio Mathematica, Vol. XLVI, no 2, 2013, 405-413. We also rectify the erratic theorems by employing a proper setting.

This article, titled "Pi: A Perpetual Journey," explores the mathematical concept of pi and its significance. The author describes pi as a never-ending and mysterious number that appears in various landscapes and civilizations. Pi is characterized by its transcendence and irrationality, and it contains a universe of patterns and prime numbers. The article also mentions different mathematical approaches to understanding pi, such as inscribed polygons and infinite series. Overall, the article presents pi as a fascinating and inexhaustible topic in mathematics. [Extracted from the article]

In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245. [ABSTRACT FROM AUTHOR]

In this paper, we show that generalized Meir-Keeler type contractive definitions are strong enough to generate a fixed point but do not force the mapping to be continuous at the fixed point. Thus we provide more answers to the open question posed by B.E. Rhoades in the paper Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245. [ABSTRACT FROM AUTHOR]

This paper points out several remarks on the paper of Pathak and Rai H. K. Pathak and D. Rai, Common fixed point theorems for PD-operator pairs under relaxed conditions with applications, J. Comput. Appl. Math. 239(2013), 103-113. In fact, under contractive conditions (assumed in the above paper), proving the existence of a common fixed point by assuming the notion of a PD-operator is equivalent to proving the existence of common fixed point by assuming the existence of a common fixed point. [ABSTRACT FROM AUTHOR]