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Very recently, I. Altun, M. Aslantas and H. Sahin [1] introduced the notion of p -proximal contractions and surveyed the existence of best proximity points for such class of non-self mappings in metric spaces. In this note we show that this existence result is a straightforward consequence of the same conclusion in fixed point theory. [ABSTRACT FROM AUTHOR]

Let A be a group acting on a p-group P coprimely. We show that if A centralizes some specified abelian subgroups of P, then A acts trivially on P. As a consequence of this, we obtain that the special rank of CP(A) is strictly less than that of P unless the action of A on P is trivial. Secondly, we prove that if A acts on a group G coprimely and [ G , A ] = G , then the exponent of C G (A) / (C G (A)) ′ divides | G : C G (A) | . [ABSTRACT FROM AUTHOR]

The main result of this paper is a fixed point theorem of self-mappings in Menger spaces which satisfy certain inequality. This inequality involves a class of real functions which we call Φ-functions. As a corollary we obtain a result in the corresponding metric spaces. The result is supported by an example. The class of real functions we have used is the conceptual extension of altering distance functions used in metric fixed point theory. [ABSTRACT FROM AUTHOR]

We extend the notion of R-weak commutativity and its variants to probabilistic metric spaces and prove common fixed point theorems concerning them. Examples are included to reflect upon the distinctiveness of the types of mappings defined in the paper. [ABSTRACT FROM AUTHOR]

We prove existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition defined in strictly convex Menger P M - spaces. [ABSTRACT FROM AUTHOR]

We give a proof for the common fixed point theorem of Jungck in rectangular b-metric spaces. As a corollary, we obtain well known common fixed point theorems in b-metric spaces. [ABSTRACT FROM AUTHOR]

We prove some stability results for the equation in the class of functions mapping a groupoid ( X, ∗) into a Banach space Y , where $${p, q, r, s: X \rightarrow X}$$ are endomorphisms of the groupoid, and A, B, C, D are fixed scalars. Particular cases of the equation are the equation of the p-Wright affine functions, the additive Cauchy equation, the Jensen equation, the quadratic equation and the general linear equation (in two variables). [ABSTRACT FROM AUTHOR]

We present a multivalued nonlinear fixed point theorem in an E-metric space introducing the concept of strict positivity in a Riesz space. Our result extends some well-known fixed point theorems obtained by J. Matkowski, R. Wȩgrzyk, R. Cristescu, and C. Çevik, I. Altun. [ABSTRACT FROM AUTHOR]

We present some general properties of solutions of an equation which appeared in a problem posed by Z. Boros and Z. Daróczy. Using them we solve this equation in some classes of functions assuming regularity of solutions. We also present some facts concerning regular solutions of two related equations. [ABSTRACT FROM AUTHOR]

Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in multi- C ternary algebras and of derivations on multi- C ternary algebras for the additive functional equation [ABSTRACT FROM AUTHOR]

We prove new common fixed point theorems for weakly compatible mappings on uniform spaces. Also, an application to locally convex spaces is presented. [ABSTRACT FROM AUTHOR]

Amini-Harandi proved that alternate convexically nonexpansive mappings on non-empty weakly compact convex subsets of strictly convex Banach spaces have fixed points. We prove that Amini-Harandi's result holds also in Banach spaces with the Kadec--Klee property and the result is true for a larger class of mappings. Moreover, we show that the Alspach mapping in L 1[0,1] is not a 2-alternate convexically nonexpansive mapping. [ABSTRACT FROM AUTHOR]