## Abstract

In this paper we study *ϕ*-recurrence *τ* -curvature tensor in (*k, µ*)-contact metric manifolds.

In this paper we study *ϕ*-recurrence *τ* -curvature tensor in (*k, µ*)-contact metric manifolds.

In this paper we derive a sequence from a movement of center of mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.

We consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂ* ^{n}* based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces

We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the *L ^{p}*-sense is

In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced (0, 2)-tensor on the tangent bundle using these structures and Liouville 1-form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

In this paper, we introduce the Mus-Sasaki metric on the tangent bundle *T M* as a new natural metric non-rigid on *T M*. First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar curvature.

The *q*-derivative operator approach is illustrated by reviewing several typical summation formulae of terminating basic hypergeometric series.

In this article, we first presented a new identity concerning differentiable mappings defined on *m*-invex set via *k*-fractional integrals. By using the notion of generalized relative semi-(*r*;*m,p,q,h*
_{1},*h*
_{2})-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard type inequalities via *k*-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

In this paper, we prove some common coupled fixed point theorems for mapping satisfying a nonlinear contraction in *S _{b}*-metric space and some results are also given in the form of corollary. Also, some examples are given to verify the main results.