Several bounds of trigonometric-exponential and hyperbolic-exponential type for sinc and hyperbolic sinc functions are presented. In an attempt to generalize the results, some known inequalities are sharpened and extended. Hyperbolic versions are also established, along with extensions.

Recently, Bród introduced a new Jacobsthal-type sequence which is called r-Jacobsthal sequence in current study. After defining the appropriate r-Jacobsthal–Lucas sequence for the r-Jacobsthal sequence, we obtain some properties of these two sequences. For simpler results, we define two new sequences and examine their properties, too. Finally, we generalize some well-known identities.

In this paper we formulate a setvalued fixed point problem by combining four prevalent trends of fixed point theory. We solve the problem by showing that the set of fixed points is nonempty. Further we have a data dependence result pertaining to the problem and also a stability result for the fixed point sets. The main result is extended to metric spaces with a graph. The results are obtained without the use of metric completeness assumption which is replaced by some other conditions suitable for solving the fixed point problem. There are some consequences of the main result. The main result is illustrated with an example.

We consider two variants of the sine subtraction law on a semigroup S. The main objective is to solve f(xy^*) = f(x)g(y) - g(x)f(y) for unknown functions f,g: S→ℂ, where x↦x^* is an anti-homomorphic involution. Until now this equation was not solved even when S is a non-Abelian group and x^* = x^-1. We find the solutions assuming that f is central. A secondary objective is to solve f(xσ(y)) = f(x)g(y) - g(x)f(y), where σ: S→S is a homomorphic involution. Until now this variant was solved assuming that S has an identity element. We also find the continuous solutions of these equations on topological semigroups.

We examine the multiplicity of the greatest prime factor in k-full numbers and k-free numbers. We generalize a well-known result on greatest prime factors and obtain formulas related with the Riemann zeta function.

In this research we introduce the concept of strong m-convexity for set-valued functions defined on m-convex subsets of real linear normed spaces, a variety of properties and examples of these functions are shown, an inclusion of Jensen type is also exhibited.

We propose in this study, a new logarithmic barrier approach to solve linear semidefinite programming problem. We are interested in computation of the direction by Newton’s method and of the displacement step using minorant functions instead of line search methods in order to reduce the computation cost.
Our new approach is even more beneficial than classical line search methods. This purpose is confirmed by some numerical simulations showing the effectiveness of the algorithm developed in this work, which are presented in the last section of this paper.

In order to explore the Leonardo sequence, the process of complexification of this sequence is carried out in this work. With this, the Gaussian and octonion numbers of the Leonardo sequence are presented. Also, the recurrence, generating function, Binet’s formula, and matrix form of Leonardo’s Gaussian and octonion numbers are defined. The development of the Gaussian numbers is performed from the insertion of the imaginary component i in the one-dimensional recurrence of the sequence. Regarding the octonions, the terms of the Leonardo sequence are presented in eight dimensions. Furthermore, the generalizations and inherent properties of Leonardo’s Gaussians and octonions are presented.