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In this paper, we are interested in obtaining fixed point theorems by keeping the orthogonal completeness of the orthogonal metric space and replacing the [Formula: see text]-contraction condition in theorems by another slightly modified conditions. The paper contains an example illustrating our results.

The question of a non-[Formula: see text]-type [Formula: see text] sequence wherein the fourth term shares the property [Formula: see text] with the first term has not been investigated so far. The present paper seeks to fill up the gap in this unexplored area. Let [Formula: see text] denote the set of all natural numbers and [Formula: see text] the sequence of Fibonacci numbers. Choose two integers [Formula: see text] and [Formula: see text] with [Formula: see text] such that their product increased by [Formula: see text] is a square [Formula: see text]. Certain properties of the sequence [Formula: see text] defined by the relation [Formula: see text] are established in this paper and polynomial expressions for Diophantine quadruples from the [Formula: see text] sequence [Formula: see text] are derived. The concept of a near-Diophantine quintuple is introduced and it is proved that there exist an infinite number of near-Diophantine quintuples.

In this paper, we present a fixed point theorem for multivalued mappings satisfying new inequalities without using the Pompeiu–Hausdorff distance. The results generalize the famous Feng and Liu’s result [Feng and Liu, J. Math. Anal. Appl. 317 (2006) 103–112] and some known results in the literature. Some examples are given to illustrate our results.

Our purpose in this paper is to investigate commutativity of a ring with involution [Formula: see text] which admits a generalized derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Moreover, we provide examples to show that the assumed restrictions cannot be relaxed.

In this paper, we gives lower and upper bounds on the covering radius of codes over [Formula: see text], where [Formula: see text] is a prime integer with respect to Lee distance. We also determine the covering radius of various Repetition codes over [Formula: see text], where [Formula: see text] is a prime integer.

In this paper, we introduce the concept of algebra cone generalized [Formula: see text]-metric space over Banach algebra by replacing the constant [Formula: see text] with [Formula: see text] where [Formula: see text] is the spectral radius of [Formula: see text], with this modification we shall prove Banach and Kannan fixed point results for contractive generalized Lipschitz mappings in such a space. Moreover, we present one example in support of our results.

Let [Formula: see text] be a simple graph. A hop dominating set [Formula: see text] is called a connected hop dominating set of [Formula: see text] if the induced subgraph [Formula: see text] of [Formula: see text] is connected. The smallest cardinality of a connected hop dominating set of [Formula: see text], denoted by [Formula: see text], is called the connected hop domination number of [Formula: see text]. In this paper, we characterize the connected hop dominating sets in the join, corona and lexicographic product of graphs and determine the corresponding connected hop domination number of these graphs. The study of these concepts is motivated with a social network application.

The tensor product and the Cartesian product of two graphs are very well-known graph products and studied in detail. Many graph parameters, particularly independence number, have been studied for these graph products. These two graph products have been generalized by [Formula: see text]-tensor product and [Formula: see text]-Cartesian product, respectively, and studied in detail. In this paper, we discuss the independence number for [Formula: see text]-tensor product [Formula: see text] and [Formula: see text]-Cartesian product [Formula: see text]. In general, we obtain lower bound and upper bound for the independence number.

In this paper, we show some Second Main Theorems for zero-order meromorphic mappings intersecting slowly moving targets in [Formula: see text] by considering their [Formula: see text]-Casorati determinant. Our results are [Formula: see text]-difference analogues of Cartan’s Second Main Theorem for moving targets. As an application, we give an unicity theorem for meromorphic mappings of [Formula: see text] into [Formula: see text] under the growth condition “order [Formula: see text]”.

In this paper, we introduce the concept of generalized [Formula: see text]-Suzuki-contractions in the context of quasi [Formula: see text]-metric-like spaces and we establish some related fixed point theorems. As consequences, we obtain some known fixed point results in the literature. Some concrete examples are also provided illustrating the obtained results.

By the use of the celebrated Kato’s inequality, we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space [Formula: see text] Natural applications for functions defined by power series of normal operators are given as well.

The fractional derivative operator is an extension of the usual derivative operator [Formula: see text] to an arbitrary (integer, rational, irrational or complex) values of [Formula: see text]. In this paper, weighted fractional differentiation composition operators from mixed-norm spaces to Zygmund spaces are characterized in terms of boundedness and compactness.

In this paper, we generalize Nadler’s result by establishing the existence and uniqueness of coincidence and common fixed points of Nadler’s type set-valued mappings in ultrametric spaces. Examples are given to illustrate the results. As an application, well-posedness of a common fixed point problem is proved. The presented results generalize many known results in literature in the framework of ultrametric spaces.

In this paper, we introduce the concept of set-valued Prešić–Reich type contractive condition in ultrametric spaces and establish the existence and uniqueness of coincidence and common fixed point of a set-valued and a single-valued mapping besides furnishing illustrative examples to highlight the realized improvements in the context of ultrametric spaces. Our results generalize and extend some known results in the literature.

Given a group [Formula: see text], we study right and left zeros, idempotents, the minimal ideal, left cancelable and right cancelable elements of the semigroup [Formula: see text] of [Formula: see text]-linked upfamilies and characterize groups [Formula: see text] whose extensions [Formula: see text] are commutative. We finish the paper with the complete description of the structure of the semigroups [Formula: see text] for all groups [Formula: see text] of cardinality [Formula: see text].

An involuted semilattice [Formula: see text] is a semilattice [Formula: see text] with an identity element [Formula: see text] and with an involution [Formula: see text] satisfying [Formula: see text] and [Formula: see text]. We consider involuted semilattices [Formula: see text] with an identity [Formula: see text] such that there is a subsemilattice [Formula: see text] without [Formula: see text] with the property that any [Formula: see text] belongs to exactly one of the following four sets : [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text]. In this paper, we introduce an associative binary operation [Formula: see text] on [Formula: see text] in the following quite natural way: [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text] and characterize all endomorphisms of the orthodox semigroup [Formula: see text].

This paper deals with the multiple values and algebraic dependences problem of meromorphic mappings sharing moving hyperplanes in projective space. We give some algebraic dependences theorems for meromorphic mappings sharing moving hyperplanes without counting multiplicity, where all zeros with multiplicities more than a certain number are omitted. Basing on these results, some unicity theorems regardless of multiplicity for meromorphic mappings in several complex variables are given. These results are extensions and strong improvements of some recent results.

In this paper, assuming an appropriate condition, we prove that [Formula: see text]-generalized hybrid mappings are demiclosed in Hilbert spaces. Using this fact, we prove a weak convergence theorem of Ishikawa type for these nonlinear mappings. Also, a strong convergence theorem of Halpern–Ishikawa type and a nonlinear ergodic theorem for [Formula: see text]-generalized hybrid mappings have been proven in Hilbert spaces.

In this paper, we introduce the neighborhood [Formula: see text] of analytic functions [Formula: see text] and [Formula: see text] defined in the open unit disc. Furthermore, we derive some sufficient and necessary conditions to be in [Formula: see text]. In addition, we see some applications of Jack’s lemma.

The reciprocal complementary distance (RCD) matrix of a graph [Formula: see text] is defined as [Formula: see text], in which [Formula: see text] if [Formula: see text] and [Formula: see text] if [Formula: see text], where [Formula: see text] is the diameter of [Formula: see text] and [Formula: see text] is the distance between the [Formula: see text]th and [Formula: see text]th vertex of [Formula: see text]. The [Formula: see text]-energy [[Formula: see text]] of [Formula: see text] is defined as the sum of the absolute values of the eigenvalues of RCD-matrix of [Formula: see text]. Two graphs [Formula: see text] and [Formula: see text] are said to be RCD-equienergetic if [Formula: see text]. In this paper, we obtain the RCD-eigenvalues and RCD-energy of the join of certain regular graphs and thus construct the non-RCD-cospectral, RCD-equienergetic graphs on [Formula: see text] vertices, for all [Formula: see text].

The purpose of this paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Poisson distribution series. To be more precise, we investigate such connections with the classes of analytic univalent functions [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in the open unit disc [Formula: see text].

In a graph [Formula: see text], a non-empty set [Formula: see text] is said to be an open packing set if no two vertices of [Formula: see text] have a common neighbor in [Formula: see text] Let [Formula: see text] and let [Formula: see text] denote the maximum cardinality of an open packing set in [Formula: see text] which contains [Formula: see text]. Then [Formula: see text] is called the open packing saturation number of [Formula: see text]. In this paper, we initiate a study on this parameter.

In this paper a method to construct a global sheaf space over a topological space for an arbitrary set using tolerance relations is proposed. It is observed that in general, the sheaf constructed by this method is different from the sheaf constructed by the method discussed in [U. M. Swamy, Representation of Universal algebra by sheaves, Proc. Amer. Math. Soc. 45 (1974) 55–58]. A necessary and sufficient condition for embedding a non-empty set into the set of all global sections of a sheaf over given topological space is established, and further an application over graphs is studied.

Known and new results on identities of an [Formula: see text]-ary group are studied in this paper.

In this paper, we introduce and investigate some inclusion theorems, convolution theorems and class preserving transforms for subclasses of the meromorphic multivalent function associated with the El-Ashwah operator. Some interesting corollaries and consequences of the main results are pointed out.

In this paper, we prove that regular paramedial division groupoids and binary regular paramedial division algebras are linear over an abelian group. Using this results we prove that every finitely generated paramedial division groupoid is a quasigroup and that every paramedial division groupoid is a homomorphic image of a paramedial quasigroup.