We study sharp growth conditions for the boundedness of Hardy-Littlewood maximal function in generalized Orlicz spaces. assume that \(\phi(x,t)\) satisfies standard continuity properties (A0), (A1) and (A2). show if is bounded from space to itself then \(\phi(x,t)/t^p\) almost increasing large \(t\) some \(p>1\). Moreover we \(L^\phi(\mathbb{R}^n)\) only \(\phi\) weakly equivalent a \(\psi\)...

Banach contraction principle is a fundamental result in fixed point theory and has been applied and extended in many different directions. In 2002, Branciari [3] obtained a fixed point theorem for a single mapping satisfying an analogue of Banach’s contraction principle for an integral type inequality. Aliouche [2] established a common fixed point theorem for weakly compatible mappings in symme...

The aim of the present paper is to prove a common fixed point theorem for six mappings via pointwise R-weakly commuting mappings in probabilistic metric spaces satisfying contractive type implicit relations. This generalizes several known results in the literature including those of Kumar and Pant (Filomat 22:2 (2008), 43-52), Kumar and Chugh (Sci. Math. Japan. 56 (2002), 269-275) and others. M...

In this paper, first we prove common fixed point theorems for a pair of weakly compatible maps. Secondly, we prove a fixed point theorem for weakly compatible maps along with (CLRg) property. In fact, our results generalize the results of Z. Mustafa et al. [10]. 2000 AMS Classification: 47H10, 54H25

We discuss the integrability properties of the Boussinesq equations in the language of geometrical quantities defined on an appropriately chosen coset manifold connected with the W 3 algebra of Zamolodchikov. We provide a geometrical interpretation to the commuting conserved quantities, Lax-pair formulation, zero-curvature representation, Miura maps, etc. in the framework of nonlinear realizati...

Indigenous upland rice (Oryza sativa L.) is an important staple food for people. The productivity of generally lower than lowland since crop yield depends on the amount rainfall. Climate change a major problem in production due to unpredictable flowering time, maturity days, growth duration, and photoperiod sensitivity are determining productivity. Therefore, this study, indigenous germplasm wa...

We prove a unique common fixed-point theorem for two pair of weakly compatible maps in a complete metric space, which generalizes the result of Brian Fisher by a weaker condition such as weakly compatibility instead of compatibility and contractive modulus instead of continuity of maps.

The recently proven Quantum Lovász Local Lemma generalises the well-known Lovász Local Lemma. It states that, if a collection of subspace constraints are “weakly dependent”, there necessarily exists a state satisfying all constraints. It implies e.g. that certain instances of the quantum k–QSAT satisfiability problem are necessarily satisfiable, or that many-body systems with “not too many” int...

We discuss the integrability properties of the Boussinesq equations in the language of geometrical quantities defined on an appropriately chosen coset manifold connected with the W 3 algebra of Zamolodchikov. We provide a geometrical interpretation to the commuting conserved quantities, Lax-pair formulation, zero-curvature representation, Miura maps, etc. in the framework of nonlinear realizati...