Some new inequalities of Ostrowski type for functions whose derivatives are $h$-convex in modulus are given. Applications for midpoint inequalities are provided as well.

In this paper the concepts of lacunary vector valued double sequences and $\Delta_{11}$-lacunary statistical convergent vector valued double difference sequences have been introduced. Further, the purpose of this work is to extend the known sequence space in the literature for ordinary single sequences to the double sequence space $\Delta_{11}N_{\theta_{r,s}}(E)$ of lacunary strongly convergent vector valued double sequences. Some inclusion relations among them are also established. Lastly, this paper deals with some results which establish the relationship between various lacunary methods.

In this paper, we prove that for any positive integer $p$, when $p \equiv 1\pmod{6}$ or, $p \equiv 3 \pmod{6}$, the Diophantine equation: $2^p A^6 + B^3 = C^2$ has infinitely many co-prime integral solutions $A$, $B$, $C$. When $p=0$, this equation has only four integral solutions with $(A, B, C)= (\pm1,2,\pm3)$. For other integer values of $p$, the problem is open.

In this paper, a Lotka-Volterra functional differential equation is considered. By establishing a nonlinear nonautonomous delay differential inequality and using a generalized Barbǎlat's lemma, we obtain some new sufficient conditions ensuring the dissipativity of the Lotka-Volterra functional differential equation.

The notion of $(X, \preceq)$ partially ordered set is well known and its study for fixed points is well entrenched in the literature. In this manuscript, we obtain sufficient conditions for the existence of common fixed point for two set valued mappings satisfying an implicit relation in complete $G$-metric space on partially ordered set $X$.

In this paper, we establish some new modular equations of degree 9. We also establish several new $P$--$Q$ mixed modular equations involving theta–functions which are similar to those recorded by Ramanujan in his notebooks. As an application, we establish some new general formulas for explicit evaluations of a remarkable product of theta--functions.

Based on the concept of accessible subhemirings and inspired by the work on the general Kurosh-Amitsur radical theory for rings, this paper studies the lower radical classes and the hereditary radical classes of hemirings. We characterize radical classes of hemirings, and construct a lower radical class from a homomorphically closed class. We provide a necessary and sufficient condition under which an upper radical class of hemirings becomes hereditary and prove that an upper radical class of a regular class of semirings is hereditary. Besides, we show that the Brown-McCoy radical class and a Jacobson-type radical class are hereditary.

In this article, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a fuzzy metric space satisfying a generalized Meir-Keeler type contractive condition. Our results substantially extend, generalize, improve and fuzzify multitude of well known results of the form existing in literature in metric as well as fuzzy metric spaces.

The aim of this paper is to introduce and characterize $ps$-$ro$ semiopen (semiclosed) fuzzy sets, which are totally independent of the existing notion of fuzzy open (closed) sets and semiopen (semiclosed) fuzzy sets. Also, in term of these fuzzy sets and operators $ps$-$scl$ and $ps$-$sint$, a class of functions named as $ps$-$ro$ fuzzy semicontinuous and $ps$-$ro$ fuzzy semiopen (closed) functions are defined and their various properties are studied. $ps$-$ro$ fuzzy semicontinuity is indeed totally different from both the existing concepts of fuzzy continuity and fuzzy semicontinuity. Similarly, $ps$-$ro$ fuzzy open (closed) and well known concept of fuzzy semiopen (closed) functions do not imply each other. These concepts are used as new tools to study different characterizations of the given fuzzy topological space, giving a new dimension in the study of fuzzy topological spaces.

Does the class of linear orders have (one of the variants of) the so called $(\lambda,\kappa)$-limit model? It is necessarily unique, and naturally assuming some instances of G.C.H. we get some positive results. More generally, letting $T$ be a complete first order theory and for simplicity assume G.C.H., for regular $\lambda > \kappa > |T|$ does $T$ have (variants of) a $(\lambda,\kappa)$-limit models, except for stable $T$? For some, yes, the theory of dense linear order, for some, no. Moreover, for independent $T$ we get negative results. We deal more with linear orders.