Fixed point theorems of generalized S - β - Ψ contractive type mappings

In this paper, we introduce the concept of generalised S - β - Ψ contractive type mappings. For these mappings we prove some fixed point theorems in the setting of S-metric space

Fixed Point Results on Partial Modular Metric Space

In the present paper, we refine the notion of the partial modular metric defined by Hosseinzadeh and Parvaneh to eliminate the occurrence of discrepancies in the non-zero self-distance and triangular inequality. In support of this, we discuss non-trivial examples. Finally, we prove a common fixed-point theorem for four self-mappings in partial modular metric space and an application to our result; the existence of a solution for a system of Volterra integral equations is discussed

<i>C</i>*-Algebra-Valued Partial Modular Metric Spaces and Some Fixed Point Results

In the present paper, we introduce the notion of C*-algebra-valued partial modular metric space satisfying the symmetry property that generalizes partial modular metric space, C*-algebra-valued partial metric space, and C*-algebra-valued modular metric space and discuss it with examples. Some fixed point results using (ϕ,MF)-contraction mapping are discussed in such space. In addition, we study the stability of obtained results in the spirit of Ulam and Hyers. As an application, we also provide the existence and uniqueness of the solution for a system of Fredholm integral equations

Table_1_Elucidating the impact of boron fertilization on soil physico-chemical and biological entities under cauliflower-cowpea-okra cropping system in an Eastern Himalayan acidic Inceptisol.docx

Information on the role of boron (B) on soil physico-chemical and biological entities is scarce, and the precise mechanism in soil is still obscure. Present field investigation aimed to assessing the implication of direct and residual effect of graded levels of applied-B on soil biological entities and its concomitant impact on crop productivity. The treatments comprised of five graded levels of B with four replications. To assess the direct effect of B-fertilization, cauliflower was grown as a test crop wherein, B-fertilization was done every year. For assessment of succeeding residual effects of B-fertilization, cowpea and okra were grown as test crops and, B-fertilization was phased out in both crops. The 100% recommended dose of NPK (RDF) along with FYM was uniformly applied to all crops under CCOCS. Results indicated that the direct effect of B had the edge over residual effect of B in affecting soil physico-chemical and biological entities under CCOCS. Amongst the graded levels of B, application of the highest B level (2 kg ha–1) was most prominent in augmenting microbiological pools in soil at different crop growth stages. The order of B treatments in respect of MBC, MBN, and soil respiration at different crop growth stages was 2.0 kg B ha–1 > 1.5 kg B ha–1 > 1.0 kg B ha–1 > 0.5 kg B ha–1 > 0 kg B ha–1, respectively. Moreover, maximum recoveries of potentially mineralizable-C (PMC) and potentially mineralizable-N (PMN) were noticed under 2 kg B ha–1. Analogous trend was recorded in soil microbial populations at different crop growth stages. Similarly, escalating B levels up to 2 kg B ha–1 exhibited significantly greater soil enzymatic activities viz., arylsulphatase (AS), dehydrogenase (DH), fluorescein diacetate (FDA) and phosphomonoesterase (PMA), except urease enzyme (UE) which showed an antagonistic effect of applied-B in soil. Greater geometric mean enzyme activity (GMEA) and soil functional diversity index were recorded under 2 kg B ha–1 in CCOCS, at all crop growth stages over control. The inclusive results indicated that different soil physico-chemical and biological properties CCOCS can be invariably improved by the application of graded levels of B up to 2 kg B ha–1 in an acid Inceptisol.</p