# Mathematica Moravica, Vol. 12-1 (2008)

Coincidence and Common Fixed Point Theorems for Hybrid Mappings
Mathematica Moravica, Vol. 12-1 (2008), 1–13.

Abstract. We prove common fixed point theorems for two pairs of hybrid mappings satisfying implicit relations in metric spaces using the concept of $T$-weak commutativity and we correct errors of [1], [4], [5] and [12]. Our Theorems generalize results of [1-5], [12] [16], [17-20] and [26].
Keywords. Hybrid mappings, common fixed point, $T$-weakly commuting, metric space.

Not on Sequence of Exponents of SO-Regular Variability
Mathematica Moravica, Vol. 12-1 (2008), 15–18.

Abstract. In this paper we develop the concept of the sequence of exponents of $SO$-regular variability [9], as a generalization of the sequence of convergence exponents [1].
Keywords. Regular variability, sequence of exponents of convergence.

Totally Umbilical Semi-Invariant Submanifolds of a Nearly Sasakian Manifold
Mathematica Moravica, Vol. 12-1 (2008), 19–24.

Abstract. We have studied some differential geometric aspects of semi-invariant submanifolds of a nearly Sasakian manifold, which led us to classify of totally umbilical semi-invariant submanifolds of a nearly Sasakian manifold.
Keywords. Semi-invariant, totally umbilical, nearly Sasakian.

Common Fixed Points for Generalized Affine and Subcompatible Mappings with Application
Mathematica Moravica, Vol. 12-1 (2008), 25–36.

Abstract. Common fixed point results for generalized affine mapping and a class of $\mathcal{I}$-nonexpansive noncommuting mappings, known as, subcompatible mappings, satisfying (E.A) property have been obtained in the present work. Some useful invariant approximation results have also been determined by its application. These results extend and generalize various existing known results with the aid of more general class of noncommuting mappings, Ciric's contraction type condition and generalized affine mapping in the literature.
Keywords. Best approximation, weakly compatible maps, subcompatible maps, property (E.A), generalized affine map, generalized affine map.

A Note about the Pochhammer Symbol
Mathematica Moravica, Vol. 12-1 (2008), 37–42.

Abstract. In this paper we give elementary proofs of the generating functions for the Pochhammer symbol $\{(i)_{n}\}_{i=0}^{\infty}, n\in N$.
Keywords. Pochhammer symbol, generating function, Direchlet series, Riemann zeta function, Stirling number, falling factorial.

Common Fixed Point Theorems for Finite Number of Mappings without Continuity and Compatibility on Fuzzy Metric Spaces
Mathematica Moravica, Vol. 12-1 (2008), 43–61.

Abstract. The aim of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on noncomplete fuzzy metric spaces. We improve extend and generalize several fixed point theorems on metric spaces, uniform spaces and fuzzy metric spaces. We also give formulas for total number of commutativity conditions for finite number of mappings.
Keywords. Fuzzy metric spaces, noncompatible mappings, common fixed points.

General Convexity, General Concavity, Fixed Points, Geometry, and Min-Max Points
Mathematica Moravica, Vol. 12-1 (2008), 63–109.

Abstract. This paper continues the study of general convexity and general concavity which are described in an abstract form on arbitrary sets. The main feature is the systematic use of a very versatile technique introduced in this paper via ATM-maps and MTM-maps. In this sense we give simplest applications of ATM-maps and MTM-maps to fixed point theory, geometry, variational inequalities, and mini-max theory.
Keywords. General convex structures, general convex topological spaces, fixed point theorem, Browder-Göhde-Kirk theorem, normal structure, Šmulian property, general nonexpansive mappings, ATM-maps, MTM-maps, geometry, variational inequality, min-max points, theory of KKM-maps, von Neumann's theory, general convexivity, general concavity.

The Main eigenvalues of the Seidel Matrix
Mathematica Moravica, Vol. 12-1 (2008), 111–116.

Abstract. Let $G$ be a simple graph with vertex set $V(G)$ and $(0,1)$-adjacency matrix $A$. As usual, $A^{\ast}(G) = J-I-2A$ denotes the Seidel matrix of the graph $G$. The eigenvalue $\lambda$ of $A$ is said to be a main eigenvalue of $G$ if the eigenspace $\varepsilon(\lambda)$ is not orthogonal to the all-1 vector $\mathbf{e}$. In this paper, relations between the main eigenvalues and associated eigenvectors of adjacency matrix and Seidel matrix of a graph are investigated.
Keywords. Graph spectra, main eigenvalues, Seidel matrix.

Erratum to “Diametral Contractive Mappings in Reflexive Banach Spaces”
Mathematica Moravica, Vol. 12-1 (2008), p. 117.