Volume 18, Issue 1

Abstract. In this paper we discuss partial regularity results concerning local minimizers of variational integrals of the form where a and b are N -functions of rather general type. We prove partial regularity results under quite natural conditions between a and b . Furthermore we can extend this to the non-autonomous situation which finally leads to the study of minimizers of the functional where p and q are Lipschitz-functions.

Abstract. We prove some new results on the existence of common fixed points for nonexpansive and asymptotically nonexpansive mappings in the framework of convex metric spaces. We also obtain some results on common fixed points from the set of best and best simultaneous approximations as applications. The proved results generalize and extend some of the known results in the literature.

Abstract. The paper suggests sharp norm estimates for the matrix logarithm and for the difference of the logarithms of two matrices.

Abstract. In this paper, we construct a new iterative scheme by hybrid methods to approximate a common element in the fixed points set of an infinite family of relatively quasi-nonexpansive mappings, the solutions set of a variational inequality problem and the solutions set of a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the three sets. We give several applications of our results in a Banach space. Our results extend many known recent results in the literature.

Abstract. A refinement of Steinhaus' theorem on the algebraic sum of subsets of due to Raikov (1939) was not known to the mathematical community and still is not popular. In 1994, Tadeusz Świa̧tkowski, being not aware of the existence of Raikov's theorem, proved another result of this type. Unfortunately, a few days later he passed away. In this paper we present the theorems of Świa̧tkowski and Raikov and we apply them in the theory of subadditive type inequalities. An improvement of a converse of Minkowski's inequality theorem is presented.

Abstract. We present the generalized Stokes theorem for -linear forms on Lie algebroids (which can be non-local). The Stokes formula on forms is applied to prove that two homotopic homomorphisms of Lie algebroids imply the existence of a chain operator joining their pullback operators.

Abstract. In this paper, we introduce and investigate a new class of multivalent functions by using the Hadamard product structure defined in the open unit disk. We obtain coefficient estimates, a distortion theorem, extreme points and criteria of starlikeness and convexity for functions which belong to our class. Relevant connections of the results with those obtained in earlier works are also pointed out.

Abstract. The result that the upper half plane is not preserved in the hyperbolic case has implications in physics, geometry and analysis. We discuss in details the introduction of projective coordinates for the EPH cases. We also introduce an appropriate compactification for all the three EPH cases, which results in a sphere in the elliptic case, a cylinder in the parabolic case and a crosscap in the hyperbolic case.

Abstract. In this paper, we obtain a result concerning the location of zeros of a polynomial , where are complex coefficients and z is a complex variable. We obtain a ring shaped region containing all the zeros of a polynomial involving binomial coefficients and -Fibonacci numbers. This result generalizes some well-known inequalities.